Geodesic
Inverse problem for a~third order Fredholm integro-differential equation with degenerate kernel
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 2, pp. 76-85

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It is considered the questions of one value solvability of the inverse problem for a third order nonlinear partial Fredholm type integro-differential equation with degenerate kernel. The method of degenerate kernel for second kind Fredholm integral equations is modified for the case of third order partial Fredholm type integro-differential equation. The Fredholm type integro-differential equation is reduced to a system of algebraic equations. By the aid of additional condition it is obtained a second kind nonlinear Volterra type integral equation with respect to main unknown function and a first kind linear Volterra type integral equation with respect to restore function. It is used the method of compressing maps, which gave us the real method of finding the solutions – the method of successive approximations. Further is defined the restore function. 
@article{VMJ_2016_18_2_a8,
     author = {T. K. Yuldashev},
     title = {Inverse problem for a~third order {Fredholm} integro-differential equation with degenerate kernel},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {76--85},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2016_18_2_a8/}
}
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T. K. Yuldashev. Inverse problem for a~third order Fredholm integro-differential equation with degenerate kernel. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 2, pp. 76-85. http://geodesic.mathdoc.fr/item/VMJ_2016_18_2_a8/